Problem: Suppose $11^5\equiv n\pmod 9$, where $0\le n<9$.

What is the value of $n$?
Solution: We have $11\equiv 2\pmod 9$. Therefore, we have \begin{align*}
11^5 &\equiv 2^5 \\
&= 32 \\
&\equiv \boxed{5}\pmod 9.
\end{align*}